I obtain and examine the implications of one-dimensional analytic solutions for return-current losses on an initially power-law distribution of energetic electrons with a sharp low-energy cutoff in flare plasma with classical (collisional) resistivity. These solutions show, for example, that return-current losses are not sensitive to plasma density, but are sensitive to plasma temperature and the low energy cutoff of the injected nonthermal electron distribution. A characteristic distance from the electron injection site, x(sub rc), is derived. At distances less than x(sub rc) the electron flux density is not reduced by return-current losses, but plasma heating can be substantial in this region, in the upper, coronal part of the flare loop. Before the electrons reach the collisional thick-target region of the flare loop, an injected power-law electron distribution with a low-energy cutoff maintains that structure, but with a flat energy distribution below the cutoff energy, which is now determined by the total potential drop experienced by the electrons. Modifications due to the presence of collisional losses are discussed. I compare these results with earlier analytical results and with more recent numerical simulations. Emslie's 1980 conjecture that there is a maximum integrated X-ray source brightness on the order of 10(exp -15) photons per square centimeter per second per square centimeter is examined. I find that this is not actually a maximum brightness and its value is parameter dependent, but it is nevertheless a valuable benchmark for identifying return-current losses in hard X-ray spectra. I discuss an observational approach to identifying return-current losses in flare data, including identification of a return-current "bump" in X-ray light curves at low photon energies.